In order to investigate the coupled vibration response and dynamic performance optimization method of multi-stage planetary gear reducer under complex excitation, a certain type of offshore platform lifting gearbox is studied, and a dynamic lumped parameter model for four-stage planetary gear coupled system with consideration of time-varying mesh stiffness, transmission error, mesh damping, backlash, friction moment, combined stiffness and damp is established. The dynamic equation under rated condition is solved with Runge-Kutta method, and the calculated vibration response has a good agreement with experimental value. On this basis, a dynamic optimization method of multi-stage planetary coupled system is developed by harmonic balance method. A multi-objective mixed discrete optimization model is established by taking structural parameters of housing and gear set as design variables, taking total transmission ratio, practical center distance, gear strength, etc. as constraint conditions, and taking minimizing RMS value of vibration acceleration and total mass as optimization object. The optimal design variable is solved through optimization program based on the branch-bound algorithm. It shows that total mass of the optimized gear reducer decreases by 8.2%, vibration acceleration of gear set decreases by 33.4%, vibration acceleration of housing decreases by 70.5%, which indicates the optimization is effective.
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